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Exercise 7.6.2: Finding the matrix representation of a linear transformation with respect to nonstandard bases. Find [T']g for each of the given linear transformations and bases B and C. (a) T : R3 - R' defined by T 1 + 202 -203 O B = (b) T : P3 - R defined by a1 + 3a3 T (a1x3 + a2x2 + agx + a4) = a2 -5a4 B = {1, x, x + 2, 1+23); C= (c) T : P1 + P2 defined by T(aix + ao) = (a1 + 2ao)x2 - (a1 + ao)x + 300 B = {1, 1-x} , C = {1, x + 2,x2 - 1}Exercise 7.6.4: Understanding the Fundamental Theorem of Matrix Representations. Consider the linear transformation : R* -> P, defined by a1 T CL2 = 2a123 - (a1 + as)2 + 302 a3 Let u = O (a) Find Pc (T(u) ) (b) Find [TI (PB (u)) (c) Use the transformation matrix from the standard basis of R to the basis C of P3 to find T 0